AnswerSteve, Yes, transporting a refrigerator laying down, can affect the refrigerator . Basically, laying the refrigerator down, allows the oil in the compressor, and the liquid refrigerant to migrate up and into the system and can create a restriction that causes the refrigerator to not cool.
An old rule of thumb is to leave the refrigerator upright for as long as the refrigerator was laid down, or longer, before you apply power to the machine. This will allow the chemicals and oil to migrate back into the compressor, and reduce the possibility of a restriction.

AnswerDonna,
Not sure which fan you are needing but we are not showing either of the fans or compressor as being discontinued at this time. If you click on the part number listed it will show you the availability of the part. The evaporator for your unit is part number 482731, the condenser fan motor is part number 833697 and the compressor part number is W10439638.

AnswerAllen, Yes you are correct, any resistance between any compressor pin connector to chassis ground or the compressor casing would indicate a damaged winding, and the compressor would neeed to be replaced.

AnswerRichard, based on your post description, The evaporator should have an even frost/ chill pattern on the complete evaporator. Not a, heavy frost in the center, and lighter pattern on the outer edges. There are a couple of possibilities, The evaporator has a floating restriction, due to non condensables, or liquid in the evaporator. The reversing valve or solenoid could be faulty and allowing a minor heat leak, and the system could be " overcharged" creating a pressure flow issue with the refrigerant. It's doubtfull, you have a leak or an issue with the compressor. Thanks and Good Luck